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If Real Madrid were to shift from La Liga to the Premier League for some reason, I think La Liga's popularity would drop by more than half. Earlier La Liga was quite a popular league but gradually the popularity of this league decreased while the popularity of English Premier League increased. If one of the most popular clubs in the world moves to the English Premier League, I don't think anyone will follow a La Liga match. Real Madrid and Barcelona are the main reasons to follow La Liga now. And the two big clubs in La Liga are Barcelona and Real Madrid and when a match is held between these two teams, that match is the most popular match in the world of football so if a popular team moves to another league, it will naturally have a serious negative impact on that league. However, it is not known for sure whether Real Madrid will change their league, but since there are rumors, something like that could happen.
It is straight nonsense. Real Madrid won't leave La Liga, it is part of their mind games they are playing whenever La Liga is as tight at the top as it is now. They do that ever since their inception I guess. It's a strategy, put the referees and governing referee bodies under pressure in order to get less penalties against them and more penalties to their benefit. You can see how they react when Rodri won the Ballon d'Or. Real Madrid is such a fucked up club that they can't acknowledge that a great player like Rodri wins the reward and instead they decide to be disrespectful and boycott the ceremony. That is their character.
If they wanted to leave La Liga,
the FIFA, the UEFA and the governing body of any other potential league would have to approve that move. It is not going to happen because that would open the door for all other clubs to threaten with the same course of action if they feel like doing it.